Low-Rank Approximation and Regression in Input Sparsity Time

@article{Clarkson2012LowRankAA,
  title={Low-Rank Approximation and Regression in Input Sparsity Time},
  author={K. Clarkson and D. Woodruff},
  journal={Journal of the ACM (JACM)},
  year={2012},
  volume={63},
  pages={1 - 45}
}
  • K. Clarkson, D. Woodruff
  • Published 2012
  • Mathematics, Computer Science
  • Journal of the ACM (JACM)
  • We design a new distribution over m × n matrices S so that, for any fixed n × d matrix A of rank r, with probability at least 9/10, ∥SAx∥2 = (1 ± ε)∥Ax∥2 simultaneously for all x ∈ Rd. Here, m is bounded by a polynomial in rε− 1, and the parameter ε ∈ (0, 1]. Such a matrix S is called a subspace embedding. Furthermore, SA can be computed in O(nnz(A)) time, where nnz(A) is the number of nonzero entries of A. This improves over all previous subspace embeddings, for which computing SA required at… CONTINUE READING
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